One problem with imaging systems is the amount of image blur that is attributable to their optics and other components. The point-spread function (PSF) describes the response of the imaging system to a point target. The degree of broadening (blurring) of the PSF is a measure of the quality of the imaging system. Some applications require precision measurement of the system PSF to be made in-situ. This is extraordinarily difficult as it may require measuring an unresolved (near point) source at a resolution that is far higher than the pixel resolution. In some cases, it may also be necessary to measure the change in the PSF across the field-of-view (FOV) of an imaging sensor, compounding the blur-calibration problem.
In some cases, global parameter fits to a high-resolution composite image may be calculated, for example, using Zernike coefficients, to describe an input wavefront of a point-like object convolved with the active area of a pixel of the imaging system. Using Zernike coefficients, to describe an input which, when masked by optical system obscurations, ideally focused on the detector (collapsing phase and sensing power), and convolved with the detector spatial response, determines the observed image. That is, the wavefront characterizes the spatial phase across the input aperture of light coming from the source point-like object in a way that captures and characterizes the aberrations of the imaging system's optical system. The Zernike coefficients may be used to calculate the system PSF and change in the PSF across the FOV and other data products at a desired resolution and spacing. The Zernike coefficients are just one specific set of coefficients. Other coefficients based on different basis functions may also be used to describe the input wavefront and characterize the imaging system's optical aberrations.
To generate the high-resolution composite image, a controller may cause a target having a single point-like object (e.g. a pinhole) to move in the plane perpendicular to the optical axis of the system at different pixel phases across the field-of-view (FOV) of the imaging system while capturing a sequence of image frames. The sequence of image frames is then mapped to form the composite image.
However, when Zernike coefficients are calculated by fitting to the composited image there is an inherent sign ambiguity. The relative sign of the even and odd Zernike terms can be determined from the fit, the absolute sign cannot. This specifically causes a problem when interpolating Zernike coefficients from different spatial regions to determine the change in PSF across the FOV.
By comparing coefficient values fit at different focus positions, this ambiguity is removed. Inducing a known focus change induces a known change of sign in the focus term, which is even. Only one hypothesis for the absolute sign of both the even and odd coefficients will be consistent with the observed differences across multiple measurements.
To acquire data at different focus positions to remove the ambiguity, the controller causes the point target to move to different focus positions along the optical axis of the test system by translating the focus adjustment stage. At each position, the controller causes the point target to move in the plane to acquire data to generate the high-resolution composite image and compute the Zernike coefficients.
Data acquisition at multiple focus positions is time-consuming and expensive. Furthermore, final calibration of the imaging system is now dependent on the exact return of the focus adjustment stage to zero. It is generally preferred to leave test equipment focus adjustment absolutely unchanged after the test equipment is itself calibrated.
This blur-calibration problem is markedly more difficult in systems where the required precision or other conditions, such as operation in cryo-vacuum conditions, make it impractical to project precision collimated patterns that fill the sensor's entire FOV. Conventional approaches used to blur-calibrate electro-optic sensors in a cryo-vacuum chamber are time-consuming, expensive and limited in accuracy.
Thus there are general needs for systems and methods for improved blur-calibration of imaging sensors which reduce the cost and the calibration time and which increase the accuracy of the blur-calibration data. What are also needed are systems and methods for blur-calibration of imaging sensors suitable for use in cryo-vacuum conditions.